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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

The albedo effect and global warming

What the science says...

The long term trend from albedo is that of cooling. In recent years, satellite measurements of albedo show little to no trend.

Climate Myth...

It's albedo

"Earth’s Albedo has risen in the past few years, and by doing reconstructions of the past albedo, it appears that there was a significant reduction in Earth’s albedo leading up to a lull in 1997. The most interesting thing here is that the albedo forcings, in watts/sq meter seem to be fairly large. Larger than that of all manmade greenhouse gases combined." (Anthony Watts)

Change in the Earth's albedo is a potentially powerful driver of climate. When the planet's albedo or reflectivity increases, more sunlight is reflected back into space. This has a cooling effect on global temperatures. Conversely, a drop in albedo warms the planet. A change of just 1% to the Earth's albedo has a radiative effect of 3.4 Wm-2, comparable to the forcing from a doubling of carbon dioxide. So how has albedo affected global temperatures in recent decades?

Albedo trends before 2000

There are various factors that affect the Earth's albedo. Snow and ice are highly reflective so when they melt, albedo drops. Forests have a lower albedo than open land so deforestation increases albedo (but for the record, no, chopping down all our forests is not the solution to global warming). Aerosols have a direct and indirect effect on albedo. The direct effect is reflecting sunlight back into space, cooling the Earth. The indirect effect is when aerosol particles act as a cloud condensation nucleus, affecting the formation and lifetime of clouds. Clouds in turn influence global temperatures in various ways. They cool the climate by reflecting incoming sunlight but can also warm the climate by trapping outgoing infrared radiation.

All these factors are considered when adding up the various radiative forcings that drive climate. Changes in land use are calculated from historical reconstructions of cropland and pastureland changes. Combinations of satellite and surface-based observations allow us to determine trends in aerosol levels as well as cloud albedo effect. What we observe is that of the various albedo forcings, cloud albedo is the most dominant effect. The long term trend is that of cooling with a radiative forcing from 1850 to 2000 of -0.7 Wm-2.

Albedo trends after 2000

One way to measure the Earth's albedo is the use of earthshine. This is sunlight reflected from the Earth, then reflected from the Moon back to the nighttime Earth. Earthshine has been measured at the Big Bear Solar Observatory since November 1998 (with some measurements in 1994 and 1995). Figure 2 shows changes in albedo from reconstructed satellite data (black line) and Earthshine measurements (blue line) (Palle 2004).

The data in Figure 2 is problematic. The black line, reconstructed from ISCCP satellite data, "is a purely statistical parameter that has little physical meaning as it does not account for the non-linear relations between cloud and surface properties and planetary albedo and does not include aerosol related albedo changes such as associated with Mt. Pinatubo, or human emissions of sulfates for instance" (Real Climate).

Even more problematic is the spike in albedo around 2003, shown by the blue earthshine line. This is in sharp contrast to satellite measurements which showed little to no trend over the same period. To put this in perspective, consider the Pinutabo volcanic eruption in 1991 which spewed aerosols into the atmosphere. These aerosols reflected incoming sunlight, causing a negative radiative forcing of 2.5 Wm-2. This led to a dramatic drop in global temperatures. The earthshine data indicate a radiative forcing of nearly -6 Wm-2 which should cause an even greater drop in global temperatures. No such event occured (Wielicki 2007).

In 2008, the reason for the discrepancy was discovered. The Big Bear Solar Observatory installed a new telescope in 2004 to measure earthshine. With the new and improved data, they recalibrated their old data and updated their earthshine albedo results (Palle 2008). Figure 3 shows the old albedo data (black) and the updated albedo (blue). The anomalous 2003 spike disappears. Nevertheless, a trend of increasing albedo remains from 1999 to 2003.

Figure 3: Earth albedo anomalies as measured by earthshine. In black are the albedo anomalies published in 2004 (Palle 2004). In blue are the updated albedo anomalies after improved data analysis, which also include more years of data (Palle 2008).

How accurate is the earthshine method in determining global albedo? The earthshine method doesn't give a global albedo estimate. It covers about one third of the Earth at each observation occasion and certain areas can never be ‘‘seen’’ from the measurement site. Furthermore the measurements are sparsely sampled in time, and only made in a narrow wavelength band of 0.4 to 0.7 µm (Bender 2006).

In contrast, satellite data such as CERES is a global measure of the Earth’s reflected shortwave radiation, including the effects of all atmospheric and surface properties. It covers a broader spectrum than earthshine (0.3–5.0 µm). An analysis of the CERES data finds no long term trend in albedo from March 2000 to June 2005. A comparison with 3 independent sets of satellite data (MODIS, MISR and SeaWiFS) also finds "remarkable consistency" between the 4 satellite results (Loeb 2007a).

Albedo has had an effect on global temperatures - mostly a cooling effect on long term trends. As for recent albedo trends, earthshine data shows increasing albedo from 1999 to 2003 but little to no trend from 2003. Satellites show little to no trend since 2000. The radiative forcing from albedo changes in recent years appears to be minimal.

Comments

The truth is out there
Recent peer review of CERES in-flight calibration show that the CERES solar wavelength response drops in RAPs mode due to exposure to atomic oxygen. The data you show above was corrected using the rev 1 corrections described in 2009 G. Matthews, “In-flight Spectral Characterization and Calibration Stability Estimates for the Clouds and the Earth’s Radiant Energy System” Journal of Atmospheric and Oceanic Technology. Vol 26, Issue 9, pp 1685-1716. This also explains how those corrections did not account for the dimming of the on board lamps and hence over-corrected. CERES data properly calibrated would therefore show a slight drop in albedo from 2000 to 2007 as well as an increase in outgoing long wave flux (as Trenberth's climate models would expect). Read the paper and be critical, I could not fault it...

I like the site overall, but please improve this article.
The EarthShine researchers seem to be doing an honest job. For example, they compare to CERES and try to explain discrepancies. Your rebuttal seems like cherry picking and advocacy (that you elsewhere correctly pan as interfering with science.) You can do better, and I await your reply.
1. At http://www.bbso.njit.edu/Research/EarthShine/ they describe the use of two observing stations and an intermittent station. They report that their observations correlate well with satellites.
2. It's simple thermodynamics that temperature change is always and only caused by heat exchange. Temperature is an effect, not a cause. Albedo researchers are trying to measure that process on a global average. Temperature measurements are always and only point samples. If one doesn't agree with the other, that is cause for investigation, but you argue for dismissal. What's up with that?
3. What support do you have for your concluding sentence? Your paragraphs above it support a conclusion along the lines of "the temperature changes due to the albedo forcing are not shown by the reported data." But you wrote a conclusion that is a great leap away from that. I expect better at this site.
4. Even if you throw out 2003, do you admit their 2W/m/m variation in albedo forcing over 4 years, or the monthly/yearly variations in the anomoly graphs? This value is significant, compared to the GHG forcing for all emissions over the last century is estimated 2.4W/m/m.
But in this article, you write to admit only that albedo is a "potentially powerful" driver of climate. That's skepticism, not science. Are you also skeptical about CO2's potential impact? They are the same order of magnitude, certainly.
5. The EarthShine project may or may not be valuable for estimating long term trends. It's a very short data series, after all. But the short term year to year variations are natural variations, and swamp CO2 radiative forcing. At the very least, this must be estimated and controlled before drawing conclusions from short term temperature data series (30-100 years) to predict long term trends, leaving out the need to remove uncertainty before embarking on global engineering to counteract it. That's separate.
Is anyone doing this control?
6. When you write about temperature drop as "no such event occurred" and then dismiss their data aren't you engaging in the "They didn't explain everything, so their work is irrelevant" tactic of political advocacy that your website is trying to counteract?
Maybe there is mitigation by some other process or event. It is certainly a reason to investigate their methods and explain correlations or lack with other data. Looking at the BBSO bibliography I think they are doing that themselves in a more scientific way than your straw man attempts to dismiss.
Looking forward to your improvements on this one.
- Forrest

Dear Forrest, the Science Palle 2004 Earthshine manuscript is a globally discredited paper and technique. NASA have shown that even with an instrument on the Moon, due to its orbit you could not measure global albedo (as correctly stated above, also see http://science.larc.nasa.gov/ceres/STM/2005-05/loeb_earthshine.pdf ). The only global measurements are those that come from CERES when properly calibrated using peer reviewed techniques that utilize the fixed climate of the Moon as a calibration standard. These show a statistically significant drop in Earth albedo from 2000-2005 and a statistically significant increase in out going thermal radiance (see Matthews 2009). If you wish to discuss global warming, consider that. Absolutely no conclusions about climate change can or should be made based on Earthshine data. The truth is out there and its peer reviewed, hope that helps.
Moldyfox

Has it been proven that the equilibrium temperature of a body in a constant EM radiation field can be altered by altering it's reflectivity (short of perfect reflectivity﻿ where equilibrium temperature must remain undefined)?
Is it not necessary to demonstrate that in order to prove that albedo or aerosol-based reflectance can influence the global mean temperature?

Yes, Rovinpiper, changing the reflectivity of a body changes the number of photons it absorbs, thereby changing the amount of energy it absorbs. All the formulas you see for calculating equilibrium temperature depend on the energy that is absorbed, not the total of that energy plus the energy that was reflected.
It will help if you think of the more elemental mechanisms that are involved. A body emits more radiative energy the hotter that body is. The body gets hotter if it absorbs more energy. But radiation reflected off the body does not get absorbed, and therefore does not make the body hotter. So the body does not radiate more energy in response to incoming radiation that it reflected. Reflected radiation might just as well never have existed, in regards to that body's temperature.

Hi Tom,
Thanks for replying to my question. Do you have a solid source for a proof of that?
I just read about Kirchoff's Law and it seems to say that if the Earth becomes more reflective it becomes less emissive by an equal amount and so temperature remains unchanged.

Hi, Rovinpiper. Good questions you're asking.
Kirchoff's Law refers to absorptance and emissivity at the same wavelength -- i.e., an object's emissivity at a given wavelength will equal its absorptance at the same wavelength.
In the case of a planet (e.g., earth), almost all the radiation it receives from the sun is at short wavelengths (UV, visible, and near-infrared). In contrast, all the radiation it emits is at long wavelengths (> 3 micrometers).
So, a change in the earth's albedo can increase or decrease the amount of energy that is absorbed, without necessarily increasing or decreasing the amount of energy that is emitted.
When this happens, the planet then warms or cools until the outgoing radiation is once again in balance with the incoming radiation.
Hopefully that's clear. It's around midnight here and I'm not really a night person, so my explanations may not be all that coherent......

And, back to the previous question:
"Has it been proven that the equilibrium temperature of a body in a constant EM radiation field can be altered by altering it's reflectivity [...]
Is it not necessary to demonstrate that in order to prove that albedo or aerosol-based reflectance can influence the global mean temperature?"
There are actually quite a few different ways you can see this operating in the real world. If you live in a place where it snows in the winter, you might notice dirty snow melting faster than clean snow -- because its lower albedo causes it to absorb more sunlight and warm up faster.
The same principle is what makes ice ages cold ... as the large continental ice sheets expand, they reflect more sunlight back to space, which makes the local climate cooler, which helps the ice expand further. (When they begin melting, at the end of each glacial episode, the same process happens in reverse -- the loss of ice makes the landscape absorb more sunlight, making it warmer, which melts the ice further....)

Hi Ned,
There's something I don't understand in your explanation of Kirchoff's Law. You say that emissivity is equal to absorptance at any given wavelength, yet the Earth absorbs light in visible wavelengths and then emits that energy as infrared, doesn't it. How can the emissivity be equal to absorptance at the visible wavelengths if the energy is getting converted into infrared?
Thanks again.

That's a great question, Rovinpiper.
Think about an object at normal Earth temperature, and assume it's floating in a vacuum. This object has an absorptance in the visible (a_vis) and an emissivity in the visible (e_vis). It also has an absorptance in the thermal-infrared (a_tir) and an emissivity in the thermal-infrared (e_tir).
Now, Kirchoff's Law tells us that [a_vis must equal e_vis], and [a_tir must equal e_tir].
With me so far?
OK, now, as long as this object is at normal Earth temperatures, e_vis is basically irrelevant -- because it's too cold to emit anything in the visible. It still has a value for emissivity in the visible spectrum, but it never gets a chance to use that.
So, under normal conditions, the object absorbs visible solar radiation (sunlight) according to a_vis. If we assume it's floating in a vacuum, it only loses energy by emitting thermal-infrared, in proportion to e_tir.
Consider a substance familiar to most of us: paint. Typically, paint will have an emissivity of around 0.90 to 0.96 in the thermal-infrared, but the range is mostly a function of the type of paint, not its color. Anyway, that painted surface would also have an absorptance of 0.90-0.96 for thermal radiation.
But, in the visible spectrum, that painted surface might have an absorptance way below 50% (for white paint) or almost 100% (for black paint).
What about its emissivity in the visible spectrum? If you could somehow heat the painted surface up to 6000 K without changing its structure and composition, the black-painted surface would emit much more radiation than the white-painted one, because in the visible spectrum it would have a higher emissivity.
So ... to get back to your question from a few days ago -- if the Yellowstone Supervolcano were to erupt tomorrow, and eject gigatons of aerosols into the stratosphere, that would increase the Earth's albedo (reflectance) in the solar spectrum. But it wouldn't make a corresponding reduction in the Earth's thermal-infrared emissivity.
With less radiation coming in, and the same amount going out, the climate would not be at equilibrium, and things would start to get cold. The colder planet would then emit less infrared radiation, and the equilibrium would return, with the planet at a lower temperature (until all the aerosols wash out of the stratosphere...)
Let's hope that doesn't happen any time soon!

Rovinpiper,
Kirchoff's Law refers to a material's capacity to absorb and emit radiation at a specific wavelength, not the actual amount that is absorbed or emitted at that wavelength. The total amount of radiation emitted at a specific wavelength does not need to match the amount of radiation absorbed at that same wavelength. It is no violation of the law to have the majority of radiation absorbed in one wavelength while the majority of radiation emitted is in another. After all, materials don't "remember" how their energy was received.

I just realized that some people may not be that familiar with the terminology here. There's a very important distinction between
* "absorptance" and "absorbed energy"
and likewise between
* "emissivity" and "emitted energy"
"Absorptance" is a unitless fraction (from 0 to 1) that says how efficient something is at absorbing radiation. It's defined as
alpha = L_a / L_i
where L_a = absorbed energy and L_i = incident energy
Note that as L_i fluctuates, (say, as the sun rises and sets), L_a fluctuates too, but alpha stays constant.
Similarly,
M = e * s * T^4
where M, the total amount of emitted energy, is a function of emissivity (a unitless fraction from 0-1 that says how efficiently something is able to emit, compared to a blackbody) and T is temperature in kelvins.
So, the amount of energy that gets absorbed by an object (L_a) is determined by how much energy is incident on it and its innate absorptance (the unitless fraction "alpha").
Likewise, the amount of energy that gets emitted by an object (M) is determined by its temperature and its innate emissivity (the unitless fraction "e").
Okay, here's the reason I just walked through all that verbiage:
Kirchoff's law says that an object's emissivity (at a given wavelength) must be equal to its absorptance (at the same wavelength).
It does *not* say that the object's emitted energy (at a given wavelength) must be equal to its absorbed energy (at the same wavelength).
In my experience, people (i.e., undergrads in the first week of my class) can easily get tripped up by this.
Bottom line -- the amount of solar energy the Earth absorbs is determined by its shortwave albedo (alpha) and by total solar irradiance. The amount of energy the Earth emits is determined by its longwave emissivity (e) and its temperature. The two quantities are not necessarily moving in lockstep ... thus, the climate can warm or cool.

Tom, Ned, e,
Yeah, Tom. I'm a bagpiper.
Thanks for your help. Kirchoff's Law makes sense to me now.
You know, in the book "Jurassic Park", the chaos theorist character, Ian Malcolm, asserts that someone wearing black clothing will be just as comfortable as someone wearing a light color because of black body radiation. Now, Crichton's written "State of Fear". I wonder if his misconception of black body radiation is an important factor in his views on global warming.

You know, in the book "Jurassic Park", the chaos theorist character, Ian Malcolm, asserts that someone wearing black clothing will be just as comfortable as someone wearing a light color because of black body radiation.
Really? I must have missed that, though it's been a long time since I read those books.
Yes, Dr Malcolm is forgetting about the wavelength-dependence of absorptance and emissivity. Kind of surprising, given that people have known for a long time that dark-colored objects will heat up much faster in the sunlight than light-colored objects.

#16: "Dr Malcolm"
And who wrote Jurassic Park? Same guy who did this bit of work. At last we see how those deniers work, moving so seamlessly that one cannot tell where their non-fiction ends and their fiction begins.

I am facing that most intractable of global warming deniers, the old physicist. Faced with what we just discussed about Kirchoff's Law he states that we must integrate over the whole spectrum.
How do you do that?

Hi, Rovinpiper. Sorry to have missed your first question:
What is "s" in your equation for energy emitted?
It should be a "sigma" ... it's the Stefan-Bolzmann constant. Since it's constant, the equation tells us that emitted energy at a given wavelength is a function of just the object's temperature and its emissivity (fraction) at that wavelength.
[...] he states that we must integrate over the whole spectrum.
Must integrate over the whole spectrum to do what? What's he "skeptical" about?
The spectral distribution of incoming solar radiation is very different than the spectral distribution of outgoing longwave radiation. The former is almost entirely at short wavelengths (probably > 99% of it is below 3 micrometers) , while the latter is almost entirely long wavelengths (definitely > 99% of it longer than 3 micrometers). The latter is why the Earth doesn't glow in visible light (lava flows and forest fires excepted...).
So you don't really need to integrate across the entire spectrum (or integrate anything, really) to answer the questions you were talking about earlier in this thread. Changing the visible-wavelength albedo of an object will change how much it absorbs, without necessarily implying a corresponding change in the efficiency with which it emits longwave radiation. In that case, the object will warm up or cool down until it reaches a new equilibrium.
Dunno if this helps at all.

Rovinpiper
not sure I understood your mate's question. If referred to Kirchoff law, it is valid at each wavelength and need not be integrated.
Integration, instead, is performed when computing the radiative balance.

Hi Ned,
For our purposes he is "skeptical" about the ability of light-reflecting aerosols to lower Global Mean Temperature. He seems to be saying that a change in the reflectance of an object in a constant electromagnetic field will not change its equilibrium temperature. This is because the emissivity of said object will increase.
He says that his personal friend Ferenc Miskolczi has a paper positing this which has never been refuted. I have a link to Miskolczi's work. Unfortunately, the material is too complicated for me to read. It might as well be written in context free grammar as far as I'm concerned.

Read further down articles - it may be shrinking though CERES says stable. However, Flaner discussed elsewhere here indicates albedo decreasing faster than expected.
However, to the primary point of your question. Albedo (unless otherwise stated) refers to energy reflected back in visible spectrum. Obviously, this is an important feedback but the source of the energy for warming by GHG is the increase in DLR. The reduction in OLR due to increased GHG is not captured by measurement of albedo.

scaddenp,
"Read further down articles - it may be shrinking though CERES says stable. However, Flaner discussed elsewhere here indicates albedo decreasing faster than expected."
Do you have a free link to the paper? I'm not paying $18 to read it, and the summary is too vague.
"However, to the primary point of your question. Albedo (unless otherwise stated) refers to energy reflected back in visible spectrum. Obviously, this is an important feedback but the source of the energy for warming by GHG is the increase in DLR. The reduction in OLR due to increased GHG is not captured by measurement of albedo."
I understand, but it takes over 16 W/m^2 of additional power at the surface for a 3 C rise in temperature. The intrinsic absorption of 2xCO2 is only 3.7 W/m^2, so even assuming all of this is directed toward the surface, it needs to be amplified greater than 4 times over. The average gain of each W/m^2 from the Sun at the surface is about 1.6 - only about one third of that required for a 16 W/m^2 rise. 3.7 W/m^2 x 1.6 = 5.9 W/m^2 - leaving a deficit of over 10 W/m^2. The amount of the albedo from the surface is only about 23 W/m^2 according to Trenberth's diagram. That means the surface albedo would need to decrease by nearly half to get 16+ W/m^2 for a 3 C rise. That doesn't seem possible from just a 1 C global average intrinsic rise from 2xCO2 given we seem to be relatively close to minimum ice.

First, 3.7W/m2 is "effective top of troposphere forcing", so this is effectively the same as 3.7W/m2 of downward. Talking "even if all directed at surface" is misunderstanding how the forcing is calculated.
Second, sensitivity would be much lower as you suggest if there were no feedbacks. Albedo plays big role when ice sheets large, now, not so much. The other big feedback is GHG effect of water vapour.

scaddenp,
"First, 3.7W/m2 is "effective top of troposphere forcing", so this is effectively the same as 3.7W/m2 of downward. Talking "even if all directed at surface" is misunderstanding how the forcing is calculated."
For the purposes of my question, I'm willing to accept this.
"Second, sensitivity would be much lower as you suggest if there were no feedbacks. Albedo plays big role when ice sheets large, now, not so much. The other big feedback is GHG effect of water vapour."
Why is the water vapor 'feedback' not embodied in the gain of about 1.6?

Its not clear to me where you get your 1.6 from? Geometric correction? Why do you assume the solar number includes water vapour feedback when the CO2 value explicitly does not. There is little value in talking about TOA forcings if there is a feedback value included. The extent of feedback for a given forcing is the key to calculating climate sensitivity. (how many degrees of temp rise for a doubling of CO2). There is no back of the envelope way to do this - its an output from full GCM - and, yes the greatest uncertainty in the system. However, if you look at Realclimate's latest model/data comparison , you will see that AR4 values of about 3 fit well with data.

scaddenp,
"Its not clear to me where you get your 1.6 from? Geometric correction? Why do you assume the solar number includes water vapour feedback when the CO2 value explicitly does not."
How could the roughly 239 W/m^2 of post albedo power from the Sun (amplified to about 390 W/m^2 at the surface) not include the effects of water vapor 'feedback'? In other words, how could the effects of water vapor not have fully manifested over decades or even centuries? Even over a hundred years ago, the gain was still about 1.6. For what physical or logical reason would the water vapor response be radically different from each W/m^2 of power from the Sun?
"There is little value in talking about TOA forcings if there is a feedback value included. The extent of feedback for a given forcing is the key to calculating climate sensitivity. (how many degrees of temp rise for a doubling of CO2)."
I'm not referencing just "TOA forcings" - but the intrinsic forcing of 3.7 W/m^2 plus gain, which is about 5.9 W/m^2.
"There is no back of the envelope way to do this - its an output from full GCM - and, yes the greatest uncertainty in the system. However, if you look at Realclimate's latest model/data comparison , you will see that AR4 values of about 3 fit well with data."
I know what the models are outputting, but fit well with what data, specifically? I don't see anything in that link about water vapor, which you claim is a big 'feedback' I'm not accounting for.

RW1 - I am very concerned about this use of "gain" and "amplification". It suggests you are thinking about this via a very inappropriate electronic analogy. There is no "fixed gain" controlling how incoming flux translates to surface heat flux. That depends on GHG gas composition and surface temperature and a host of other elements. Your translation of 3.7 to 5.9 is plain wrong. Science of Doom has a series of lengthy articles with a lot of discussion on the actual mechanisms. I can only suggest a detailed study and throw out the "gain" concept.
As to model output. The real physics, not simplistic analogy, including the role of water vapour as a feedback are calculated in the models. The output from the model is surface temperature through time given the actual forcings of solar, GHG concentration, volcanoes etc. From the output, you work backwards from temperature to determine the value of sensitivity - which comes to about 3. The validity of the model is tested by comparing forecast surface temperature actual observed surface temperature. If the sensitivity - which involves all those feedbacks is wrong- then temperature prediction would be too. I thought this was plain in the article.

RW1 - let me expand here a bit. To see why idea of fixed gain doesnt work, consider what happens if there is no CO2. If it gets cold enough from loss of DLR and increasing albedo, then all water vapour is condensed out of atmosphere and there is no GHG effect. There is then no "gain". Likewise increasing the GHG increases your "gain". It seems to be that you are trying to use some heuristics and the Trenberth diagram to predict what the Trenberth diagram would look like with 2xCO2 from pre-industrial. You have to use the models to do this. Assuming models are correct then the changes would be like this:
No change to TOA inputs. The 3.7W/m2 for increased is CO2 is "effective" not a real change to TOA flux. You could get change in cloud and surface albedo from model results but for simplicity assume increases in one are cancelled by decrease in other. Evaporation etc also change but are minor players.
Surface OLR changes to from 390 to 406 and DLR increases from 324 to 340.
Your "gain" as you have defined it, increases from 1.63 to 1.69. What is your "gain" when you put two blankets on your bed at night instead of one?

A rise of about 1 C or 5.9 W/m^2 results in a new gain of only about 1.66 from 1.63 (396/239 = 1.66), which is a negligible increase. More importantly, it is still much less than the over 4x needed to get 16+ W/m^2 for a 3 C rise.
More importantly If the effects of the 'feedbacks'(including specifically water vapor) are not embodied in the gain, then explain why it doesn't take over 975 W/m^2 at the surface to offset the 239 W/m^2 coming in from the Sun? Then also explain why the response of 'feedbacks' on next 3.7 W/m^2 at the surface will all of the sudden be nearly 3 times greater than the response of 'feedbacks' acting on the original 98+%?

RW1 - The "gain" isn't the correct way to treat the issue, since the relative value is an output of the models, not a simplification you can use for input purposes.
A 3.7 W/m^2 imbalance at the TOA results in about 1C of surface warming (5.9 or so W/m^2 higher IR at the surface, although backradiation also increases with atmospheric warming, so that's not a direct imbalance).
And then feedbacks occur, changing levels of water vapor, long term albedo from ice melt, CO2 balance with the ocean, etc., each of which induce additional TOA imbalances and subsequent warming. Once feedbacks kick in their TOA imbalances are in addition to the original 3.7 W/m^2 forcing from doubling CO2.
As I recall, we had a ~450 post discussion, primarily on these issues with you and George White (who apparently originated this "gain" idea) - I don't believe a single person on the thread agreed with you two, for a lot of very good reasons. You might want to take that into consideration...

RW1 - the increase in "gain" (which certainly does include feedback) is 406/239 from model results. Again it seems you are trying to predict feedback (the increase in "gain"). Its a bogus procedure to say that
"gain" * increase in CO2 will be the increase backradiation. You have to calculate it properly.

scaddenp,
"RW1 - the increase in "gain" (which certainly does include feedback) is 406/239 from model results. Again it seems you are trying to predict feedback (the increase in "gain"). Its a bogus procedure to say that
"gain" * increase in CO2 will be the increase backradiation. You have to calculate it properly."
The 406 W/m^2 you quote isn't from any measurement but from model predictions from numerous assumptions that only exist in a computer. The 3.7 W/m^2 from 2xCO2 is from empirical measurement, so is the gain of about 1.6, which represents the amplification at the surface for each 1 W/m^2 of energy from the Sun.
If 3.7 W/m^2 of additional infrared from 2xCO2 is amplified to 16+ W/m^2 at the surface, why isn't the 239 W/m^2 from the Sun amplified by proportionally the same amount to over 1000 W/m^2?

KR,
"A 3.7 W/m^2 imbalance at the TOA results in about 1C of surface warming (5.9 or so W/m^2 higher IR at the surface, although backradiation also increases with atmospheric warming, so that's not a direct imbalance).
And then feedbacks occur, changing levels of water vapor, long term albedo from ice melt, CO2 balance with the ocean, etc., each of which induce additional TOA imbalances and subsequent warming. Once feedbacks kick in their TOA imbalances are in addition to the original 3.7 W/m^2 forcing from doubling CO2."
Why don't the same feedbacks occur (excluding the surface albedo) on the 239 W/m^2 from the Sun?

"Why don't the same feedbacks occur (excluding the surface albedo) on the 239 W/m^2 from the Sun?"
What makes you think they don't? There is some water vapor in the air already, is there not? Why is it there in the first place?

"so is the gain of about 1.6, which represents the amplification at the surface for each 1 W/m^2 of energy from the Sun."
Again, this is bogus way to do it. You need a certain amount of energy to get past the threshold of having any water vapour at all. With zero CO2, you would still have same sun, but snowball earth and no water vapour. Above a certain point, the solar minus albedo is strong enough to give water vapour and get that feedback. Note also that albedo feedback becomes more important at lower temperatures too. The 3.7W/m2 is calculation by the way too, but you can the verify the RTEs used to calculate it empirically.
I repeat, you have to calculate feedback with a model, not some half-baked "gain" idea. And the actual response of surface temperature to increasing CO2 gives a way to empirically estimate sensitivity (or test the sensitivity of model). 3 looks pretty good, but see the IPCC WG1 for variety of other empirical estimates.

Continuing from another thread
RW1 - I am lost at what you are trying to do here but pretty obviously, you dont lose 48W/m2 for each m2 of cloud!
You seem be trying to predict something about change in albedo associated with clouds but what about calculating the +ve change in DLR too? Clouds do both.

scaddenp (RE: 46),
(Sorry I'm late on this)
"RW1 - I am lost at what you are trying to do here but pretty obviously, you don't lose 48W/m2 for each m2 of cloud!"
According to Trenberth's numbers, you do:
Clouds cover about 2/3rds of the surface, so 341 W/m^2*0.67 = 228 W/m^2 average incident on the clouds. 79 W/m^2 divided by 228 W/m^2 = 0.34 average reflectivity of clouds. 1/3rd of the surface is cloudless, so 341 W/m^2*0.33 = 113 W/m^2 average incident on the cloudless surface. 23 W/m^2 divided by 113 W/m^2 = 0.20 average reflectivity of the cloudless surface. 0.34-0.20 = 0.14. 341 W/m^2*0.14 = 48 W/m^2 loss for each additional m^2 of cloud cover.
"You seem be trying to predict something about change in albedo associated with clouds but what about calculating the change in DLR too? Clouds do both."
I'm well aware clouds do both. The whole point is incrementally more clouds reflect away more energy than they re-direct back to the surface; thus, the energy needed to get the 16+ W/m^2 for a 3 C rise can only come from a reduced albedo.

scaddenp (RE: 46),
Let's run the numbers on how much energy incrementally more clouds trap:
If, according to Trenberth, the cloudy sky has a transmittance of 30 W/m^2, and the surface emitted through the cloudy sky is about 265 W/m^2 (396 x 0.67 = 265). 265 W/m^2 - 30 W/m^2 = 235 W/m^2 absorbed by the cloudy sky. The clear sky has a transmittance of 40 W/m^2, and the surface emitted through the clear sky is 131 W/m^2 (396 x 0.33 = 131). 131 W/m^2 - 40 W/m^2 = 91 W/m^2 absorbed by the clear sky. 91 W/m^2 divided by 131 W/m^2 = 0.69; 235 W/m^2 divided by 265 W/m^2 = 0.89. 0.89 - 0.69 = 0.20 difference between the cloudy and clear sky. 0.20 x 396 W/m^2 = 79 W/m^2 additional absorbed for each additional m^2 of cloud cover. If we assume that roughly half of the absorption and re-emission is back toward the surface (Trenberth actually has this being less than half), that comes to about 39 W/m^2, or about 10 W/m^2 less than the 48 W/m^2 reflected away.

The main point I'm getting at here is if the albedo is NOT decreasing (or has even slightly increased), where is the energy coming from that is supposed to be causing the warming? If, as you claim, an additional 3.7 W/m^2 at the surface is to become 16.6 W/m^2 then why doesn't it take more like 1075 W/m^2 at the surface to offset the 239 W/m^2 coming in from the Sun (16.6/3.7 = 4.5; 239 x 4.5 = 1075)??
Looked at from another angle: In energy balance terms, it takes about 390 W/m^2 at the surface to allow 239 W/m^2 to leave the system, offsetting the 239 W/m^2 coming in from the Sun (power in = power out). If, as you claim, it will take an additional 16.6 W/m^2 at the surface to allow an additional 3.7 W/m^2 to leave the system to restore equilibrium, then why doesn't it take 1075 W/m^2 emitted at the surface to allow 239 W/m^2 to leave the system to achieve equilibrium?
What is so special about the next few watts at the surface that the system is all of the sudden going to respond to them nearly 3 times a powerful as the original 98+%?
Furthermore, since the atmosphere cannot create any energy of its own, the remaining difference of about 10.6 W/m^2 (3.7 x 1.6 = 6 W/m^2; 16.6 - 6 = 10.6 W/m^2) can only come from a reduced albedo.
So again, where is all the energy coming from that is supposed to be causing the warming?